مجله مدل‌سازی پیشرفته ریاضی

مجله مدل‌سازی پیشرفته ریاضی

روش تفاضل متناهی مبتنی بر توابع پایه شعاعی برای معادلات دیفرانسیل جزئی تأخیری دو بعد‎‏ی

نوع مقاله : مقاله پژوهشی

نویسندگان
1 گروه ریاضی کاربردی-دانشکده علوم ریاضی-دانشگاه شهرکرد- شهرکرد- ایران
2 دانشگاه شهرکرد. دانشکده ریاضی. دکتر مجتبی فردی
چکیده
این مقاله یک روش عددی بدون شبکه محلی برای حل معادلات دیفرانسیل با مشتقات جزئی تأخیری دوبعدی ارائه می‌دهد. این روش بر پایه‌ی تفاضل متناهی تولیدشده با توابع پایه شعاعی توسعه یافته است. در گام نخست، گسسته‌سازی مکانی به‌صورت محلی و با استفاده از گره‌های پراکنده‌ی مجاور انجام می‌شود که موجب بهبود پایداری عددی می‌گردد. این فرآیند، معادله دیفرانسیل جزئی تأخیری اولیه را به دستگاهی از معادلات دیفرانسیل معمولی تأخیری نسبت به زمان تبدیل می‌کند. در ادامه، برای حل دستگاه زمانی حاصل، از یک طرح تفاضل متناهی استفاده می‌شود. به‌منظور ارزیابی دقت و کارایی روش، یک مثال عددی بررسی شده است. نتایج نشان می‌دهند که روش پیشنهادی دقت بالایی دارد و عملکرد آن با روش المان محدود گالرکین قابل مقایسه است.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

‎The‎ radial basis function-generated finite difference (RBF-FD) ‎method‎ for two-dimensional delayed PDEs

نویسندگان English

Mojtaba Fardi 1
Banafsheh Raeisi 2
1 Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
2 ‎Department of Applied Mathematics‎, ‎Faculty of Mathematical Science‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎88186-34141‎, ‎Iran.
چکیده English

This paper proposes a local meshfree numerical method for solving two-dimensional delayed partial differential equations (PDEs). The method is based on the radial basis function-generated finite difference approach. In the first step, spatial discretization is performed locally using scattered neighboring nodes, which improves numerical stability. This process transforms the original delayed PDE into a system of delay ordinary differential equations with respect to time. A finite difference scheme is then applied to solve the resulting temporal system. To assess the accuracy and efficiency of the method, a numerical example is presented. The results demonstrate that the proposed method achieves high accuracy and delivers performance comparable to that of the Galerkin finite element method‏.

کلیدواژه‌ها English

Delayed PDEs
‎Radial basis function-f‎inite difference (RBF-FD) method
Local discretization
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  • تاریخ دریافت 05 خرداد 1404
  • تاریخ بازنگری 14 مهر 1404
  • تاریخ پذیرش 13 اردیبهشت 1405